456x-34/2x=255

Solution for 456x-34/2x=255 equation:

456x-34/2x=255

We move all terms to the left:

456x-34/2x-(255)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


456x*2x-255*2x-34=0

Wy multiply elements

912x^2-510x-34=0

a = 912; b = -510; c = -34;
Δ = b2-4ac
Δ = -5102-4·912·(-34)
Δ = 384132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{384132}=\sqrt{4*96033}=\sqrt{4}*\sqrt{96033}=2\sqrt{96033}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-510)-2\sqrt{96033}}{2*912}=\frac{510-2\sqrt{96033}}{1824}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-510)+2\sqrt{96033}}{2*912}=\frac{510+2\sqrt{96033}}{1824}
$